Complete Solution of a Differential Game with Linear Dynamics and Bounded Controls

Abstract

A differential game is an appropriate mathematical model for real-life control problems, which either involve many decision-makers or contain a high degree of uncertainties. There is a rich literature devoted to the theory of differential games (see e.g. [1–5]). A zero-sum finite-horizon differential game with linear dynamics and bounded controls was studied extensively in the literature, because of its considerable meaning both in theory and applications (see e.g. [6–10] and the references therein). Important applications of this game are: a pursuit-evasion problem (see e.g. [11–14]), an airplane landing problem under windshear conditions (see [15] and references therein), and some others. Different versions of this game were analyzed in the literature. A simple example with the ideal dynamics of the players was considered in [6]. The game with a first-order